Mutual Information of Bipartite States and Quantum Discord in Terms of Coherence Information

Abstract

In relation of observable and quantum state, the entity $I_C$ from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this article its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogating" the global state about the state of the opposite subsystem is derived with detailed entropy and information gain discussion. The apparent disappearance of discord in measurement is investigated, and it is shown that it is actually shifted from between subsystems 1 and 2 to between subsystems 1 and $(2+3)$, where 3 is the measuring instrument. Finally, it is shown that the global coherence information $I_C(A_2,\rho_{12})$ is shifted into the global coherence information $I_C(A_2,\rho_{123}^f)$ in the final state $\rho_{123}^f$ of the measurement interaction.